Multiple-input multiple-output (MIMO) systems with multiple antennas at both transmitter and receiver sides have become very popular owing to the several advantages they promise to offer, including transmit diversity and spatial multiplexing [1]-[3]. It is known that the MIMO channels have a capacity that grows linearly with the minimum of the number of antennas on the transmitter and receiver sides [4]-[6]. A key component of a MIMO system is the MIMO detector at the receiver, whose job is to recover the symbols that are transmitted simultaneously from multiple transmitting antennas. In practical applications, the MIMO detector is often the bottleneck for both performance and complexity.
MIMO detectors including sphere decoder and several of its variants [8]-[13] achieve near-ML performance at the cost of high complexity. Other well known detectors including ZF (zero forcing), MMSE (minimum mean square error), and ZF/MMSE-SIC (ZF/MMSE with successive interference cancellation) detectors [14] are attractive from a complexity view point, but achieve relatively poor performance. Maximum number of transmit and receive antennas for which the performance of MIMO detectors have been reported in the literature so far is only in the range of 10 to 20 (e.g., 16 antennas for sphere decoder [8] and 12 antennas for ZF-SIC [15]).
The ZF-LAS detector for V-BLAST is shown to achieve the following gains compared to the well known V-BLAST detector (i.e., the ZF-SIC detector with ordering) under signal-to-noise ratios (SNR) and bit error rates (BER) of interest: i) for moderate number of antennas (e.g., about 30 antennas), ZF-LAS achieves complexity gain compared to ZF-SIC, and ii) for large number of antennas, ZF-LAS achieves both complexity gain as well as bit error performance gain compared to ZF-SIC. The achieved complexity gain significantly increases with increasing number of antennas due to the average per-bit complexity of O(NtNr) for ZF-LAS versus per-bit complexity of O(N2tNr) for ZF-SIC. The fact that we could show the simulation points of uncoded BER up to 10−5 in V-BLAST systems with several hundreds of antennas demonstrates the ZF-LAS detector's fantastic low-complexity attribute (which other known detectors have not been shown to possess). For large Nt, ZF-LAS not only has lesser complexity but also achieves much better diversity than ZF-SIC, which is a significant and interesting result. This practical detection feasibility could potentially trigger wide interest in the theory and implementation of large MIMO systems.
Interestingly, even for a near-term practical system like 8×8 V-BLAST system with 4-QAM and rate-½ outer turbo code (i.e., 8 bps/Hz spectral efficiency), ZF-LAS achieves a BER of 10−4 at an Eb/N0 of 6 dB with 3 turbo decoding iterations. Likewise, a 15×15 V-BLAST system with 4-QAM and rate-⅓ turbo outer code (i.e., 10 bps/Hz spectral efficiency), ZF-LAS achieves a BER of 10−5 at an Eb/N0 of just 3 dB with 3 turbo decoding iterations. The complexity involved with achieving similar performances using the well known ZF-SIC detector is comparatively very large. We also show that ZF-LAS is effective in decoding high-rate, non-orthogonal STBCs. We also present ZF/MF-LAS detectors for multicarrier CDMA. With its superiority in performance and complexity for large number of users, MF-LAS can be a powerful approach to MUD implementations in practical CDMA systems.